Invariants
| Level: | $102$ | $\SL_2$-level: | $6$ | Newform level: | $1$ | ||
| Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $6^{12}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 6F1 |
Level structure
| $\GL_2(\Z/102\Z)$-generators: | $\begin{bmatrix}17&48\\90&53\end{bmatrix}$, $\begin{bmatrix}29&64\\0&19\end{bmatrix}$, $\begin{bmatrix}83&49\\24&37\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 102.144.1-102.c.1.1, 102.144.1-102.c.1.2, 204.144.1-102.c.1.1, 204.144.1-102.c.1.2, 204.144.1-102.c.1.3, 204.144.1-102.c.1.4, 204.144.1-102.c.1.5, 204.144.1-102.c.1.6 |
| Cyclic 102-isogeny field degree: | $18$ |
| Cyclic 102-torsion field degree: | $576$ |
| Full 102-torsion field degree: | $313344$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 6.36.0.a.1 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 102.24.0.b.1 | $102$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
| 102.24.1.c.1 | $102$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 102.36.0.b.1 | $102$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 102.36.1.h.1 | $102$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 204.144.5.cf.1 | $204$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 204.144.5.cj.1 | $204$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 204.144.5.ds.1 | $204$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 204.144.5.dw.1 | $204$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 204.144.5.fo.1 | $204$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 204.144.5.fs.1 | $204$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 204.144.5.gv.1 | $204$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 204.144.5.gz.1 | $204$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 306.216.7.f.1 | $306$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 306.216.7.i.1 | $306$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 306.216.7.k.1 | $306$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 306.216.10.e.1 | $306$ | $3$ | $3$ | $10$ | $?$ | not computed |
| 306.216.13.p.1 | $306$ | $3$ | $3$ | $13$ | $?$ | not computed |